In the sheriff's office behind the courthouse, J. B. Torrence, who has been sheriff here since 1972, leans back behind his uncluttered desk and explains why Senator Cochran is considered to have a good chance of winning reelection in November in a state that, in many ways, is still Democratic.

Cochran's voting record has been a fairly conservative one, he says, and ''that's popular.'' Although ''a lot of the old-timers never voted Republican in their lifetime,'' Sheriff Torrence explains, ''the younger generation don't go by the party line.''

While local elections usually are won by Democrats in Mississippi, Republican presidential candidates Ronald Reagan, Richard Nixon, and Barry Goldwater all carried the state.

Democratic candidate Winter is hoping people will vote the party line - at least one more time. And he is counting on a heavy black-voter turnout.

But, despite being known as one who spoke out for blacks when it was not considered politically wise to do so, Winter can't be sure he'll get the 85 percent or so of the black vote he needs to go with the 1-out-of-3 white votes he hopes to get.

What is happening? In brief, the state that Mississippi political scientist John Quincy Adams calls ''the symbol of the Deep South . . . the most Dixified state of the South'' is changing.

Racial prejudices may not be a thing of the past, but blatant political appeals to racial prejudice by candidates of either party have faded. Both Democrats and Republicans have been courting the black vote with the knowledge that blacks comprise about one-third of the state's electorate.

Add to this a Republican candidate who does his homework on helping constitutents with personal problems involving the government, and the campaign gets even more interesting.

At the two-story Cochran campaign headquarters in Jackson, where donations are being tabulated by computer, W. D. Cooper, a white man who is legally blind, has stopped by to offer his help. Asked why he likes Cochran, he replies: ''He has time to spend with even me.''

A few miles to the north, Edna Range, a black mother of three, explains in the spacious den of her family's home in an affluent black neighborhood that Senator Cochran helped her father obtain a veteran's disability payment.

''He's a friend,'' she says of Cochran, and she and her husband support him for reelection.

Winter is attempting to portray his opponent as a Reaganite who most of the time (the Congressional Quarterly puts it at 71 percent) voted to support the President against the interests of many in the state, especially the poor.

''I've laid my political career on the line a number of times for trying to raise the level of life of poor people in this state,'' said Winter in a recent Monitor interview. ''I simply ask the black people of this state to compare what I have done and tried to do'' to what Senator Cochran has done. He accuses Cochran of supporting Reagan budget cuts ''at the very time we were struggling'' in Mississippi. And he says his experience as a state official makes him more knowledgeable about Mississippi's needs than Cochran, who, he says, lacks ''perspective'' on how state and federal government must cooperate.

As governor, Winter appointed a number of blacks to key posts in his administration. His efforts to give blacks a voice in state government ''could have been more,'' says Jackson State University political scientist Leslie McLemore. But, Professor McLemore explains, Winter faced pressure from conservative whites. His performance was ''a balancing act,'' McLemore says.

Cochran was not available for an interview. But his campaign director, Jamie Becker, says the senator is running on his record in Washington, which marks him as a ''conservative with a moderate tilt.'' Cochran ''has had to fight the administration to support blacks,'' Mr. Becker says.

The Cochran campaign is better financed than Winter's. The former governor says the senator is likely to raise and spend about twice as much as the Winter campaign.

But the Rev. Jesse Jackson's personal efforts to spur black voter registration in the state should help Winter.

And there will be no third candidate in the race, as there was in 1978 when Cochran was elected. In that election many blacks voted for Charles Evers, a top black leader in Mississippi, to the detriment of the white Democratic candidate.

Winter is well known throughout the state. He finished his four-year term as governor last January, and under Mississippi law could not seek a second consecutive term. He was a popular governor, most noted for obtaining passage of a much-needed educational reform package for the state.

But Winter calls himself an ''underdog'' in the Senate race. Most political analysts here agree, including syndicated columnist Bill Minor and state Treasurer Bill Cole, who worked for Governor Winter.

It may come down to how strong those old party labels still are in Mississippi. Two interviews in Brandon illustrate this:

''I'm a Democrat,'' said Henry Dent, a black, as he walked down the courthouse steps. ''When Winter was governor, he was good. lped blacks.''

But in the parking lot next to the courthouse, auctioneer H. N. Brewer stopped to explain that he is ''a conservative Democrat voting Republican.'' Mr. Brewer, who is white, says Cochran ''helps whites, colored ... anybody.''